It would then be easy to conclude that a high thermal input onto \(\eta _{ab}\)  helps Alice and Bob, although this would perhaps be hasty.
A thermal input onto \(\eta _{ab}\)  can happen in essentially two ways: Eve's preparation noise is thermal (Figure REF ), or the channel between Eve and \(\eta _{ab}\)  introduces the noise.
Commonly, the thermal channel is modelled as a beamsplitter where the “free” input receives a thermal state [1]}, [2]}.
